During the prime factorization process, what is the first step you take with a composite number?

• A. Break it down into its prime factors
• B. Divide by the smallest prime number that it evenly divides into
• C. List all possible factors
• D. Identify the largest prime factor

Answer: (B)

The first step in the prime factorization process for a composite number involves dividing it by the smallest prime number that it evenly divides into. This approach is systematic and helps simplify the number into its prime constituents gradually.

When you start with the smallest prime, typically 2, you can determine whether it is a factor of the composite number. If it is, you divide the composite number by that prime and continue the process with the quotient until you are left with a prime number. This method ensures an efficient breakdown of the composite number and helps in organizing the factors in a clear and manageable way.

Identifying prime factors by starting with the smallest prime is essential because it allows you to work through the number systematically, avoiding missed factors and ensuring that every composite number can be fully decomposed into its prime components. This foundational step is crucial for understanding the relationships between numbers and their properties in number theory.